The Mathematics of Money

72 Chapter 2 Simple Discount

exists is being sold. The simple interest loan that created this note is water under the bridge.

It is now natural to think of the note in terms of discount rather than interest.

This secondary sale divides the creditor’s role between the two banks. This can be

visualized with a time line as

Loan

date

$1,000 $1,020 $1,080

Secondary

sale

Maturity

date

Creditor:

FNNB

Creditor:

CCST

However, from your point of view as the borrower, the loan still looks like this:

Loan

date

$1,000 $1,080

Maturity

date

Even if you are aware that a sale has taken place, you could still look at the note in this way

since the sale does not affect you financially.

Example 2.3.1 Suppose that John loans Paul $20,000 for 1 year at 8% simple

interest. Three months later, John sells the note to Ringo at a simple discount rate of

7 ¾%. How much does Ringo pay for the note?

There are two different transactions to consider here: the original loan and the secondary

sale. While the question deals with the secondary sale, we fi rst have to work out the details

of the original loan. We can’t fi gure out the secondary sale price until we know the maturity

value of the note being sold.

Original loan: The original loan was made using simple interest.

I  PRT

I  ($20,000)(0.08)(1)

I  $1,600

The maturity value of the note would then be $20,000 
 $1,600  $21,600.

Secondary sale: The secondary sale is made using simple discount. Since 3 months of the origi-

nal 1-year term have already expired, the remaining term is 1 year  3 months  9 months.

D  MdT

D  ($21,600)(0.0775)(9/12)

D  $1,255.50

Subtracting this from the maturity value gives a price of $21,600  $1,255.50 

$20,344.50.

The discount rate used in a secondary sale does not necessarily have any connection to the orig-

inal interest rate. Under ordinary circumstances it is reasonable to expect that the rates would

be comparable. If the interest rate for the original loan is, say, 10%, then it stands to reason that

the rate that the secondary buyer would expect to be able to earn on the note would be in the

same ballpark. This does not necessarily have to be the case, as the next example illustrates.

Example 2.3.2 Tinker loaned Evers $997.52 for 235 days at a simple interest rate

of 6.54%. But 74 days later, he sold the note to Chance using a simple discount rate of

9.95%. How much did Chance pay for the note?

Original loan:

I  PRT

I  ($997.52)(0.0654)(235/365)

I  $42.00

Maturity Value  $997.52 
 $42.00  $1,039.52